Study of SPWM Technique & Simulation of Designed Analog Circuit (Op-Amp) Controlled Three

Phase PWM Inverter with Harmonic Reduction Nazmul Islam Raju1, Md. Shahinur Islam2, Tausif Ali3, Syed Ashraful Karim4

Department of EEE, American International University-Bangladesh (AIUB), Dhaka - 1213, Bangladesh.

Email: nazm_69@yahoo.com1, shahin_8943@yahoo.com2, tau9097@gmail.com3, syedashrafulkarim@yahoo.com4 Abstract Inverter is an obvious device to utilize the renewable energy resources. Pulse width modulation (PWM) technique is the most used technique for inverters. This paper represents the Sinusoidal PWM technique and shows how to generate PWM signal using different simple Op-Amp circuits for three phase voltage source inverter (VSI). It is a new design of Op-Amp circuit for switching the three phase PWM inverter. All the Op-Amp circuits have been simulated and their outputs have been shown step by step. This analog circuit (Op-Amp) controlled VSI has been simulated for both standalone load & high voltage sensitive loads/systems like micro-grid system and industrial machines respectively without and with transformer. The simulation results have been shown before and after harmonic reduction using a passive filter.

Keywords Op-Amp; MOSFET; inverter; VSI; SPWM; PWM; standalone load; Micro grid; Harmonics.

I. INTRODUCTION The growing energy demand around the world led us to

utilize renewable energy resources. To utilize these renewable energy resources an inverter is essential which converts DC to AC power as most of the renewable energy are found in DC form. In hybrid power system and micro grid system the use of inverter is significant. Moreover, in industrial applications, such as Single Phase and Three Phase Induction Motor, other rotating machines are used where variable frequency, variable voltage supply is needed. To vary the supply frequency and supply voltage, voltage source inverter (VSI) is used. For high efficiency DC-AC conversion and peak power tracking it must have low harmonic distortion along with low electromagnetic interference and high power factor [1]. An inverter is evaluated after design by using the inverter performance and testing standards which are IEEE 929-2000 and UL 1741 in US EN 61727 in EU and IEC 60364-7-712. The total harmonic distortion (THD) generated by the inverter is regulated by international standard IEC-61000-3-2. The total harmonic distortion (THD) of the voltage must be kept at minimum and according to recommended limit by IEEE Standard 519-1992 has to be kept at less than 5% for harmonic spectra up to 49th harmonic. For the partial load THD is generally much higher. To the standalone load system where the loads are low voltage the inverter is used

without transformer but in case of utility grid or high voltage sensitive loads (several KV) it should be used step up transformer with the inverter. In this paper at first it has been discussed about SPWM technique. Then the simulation outputs of inverter have been shown for the both low voltage & high voltage systems. Moreover a new design has been proposed which is an analog circuit (Op-Amp) controlled three phase SPWM voltage source inverter (VSI).

II. SPWM TECHNIQUE The “Sinusoidal Pulse Width Modulation (SPWM)”

technique is used to control the inverter as it can be directly controlled the inverter output voltage and frequency according to the sine function [2]. Sinusoidal pulse width modulation (SPWM) is widely used in power electronics to digitize the power so that a sequence of voltage pulses can be generated by the on and off of the power switches. The PWM inverter has been the main choice in power electronic for decades, because of its circuit simplicity and rugged control scheme. SPWM switching technique is commonly used in industrial applications or solar electric vehicle applications [3]. SPWM techniques are characterized by constant amplitude pulses with different duty cycles for each period. The width of this pulses are modulated to obtain inverter output voltage control and to reduce its harmonic content. Sinusoidal pulse width modulation is the mostly used method in motor control and inverter application [3]. In this technique three sine waves and a triangular carrier wave are used to generate PWM signal. The sinusoidal waves are called reference signal and they have 1200 phase difference with each other. The frequency of these sinusoidal waves is chosen based on the required inverter output frequency (50/60 Hz). The carrier triangular wave is usually a high frequency (in KHz) wave. The switching signal is generated by comparing the sinusoidal waves with the triangular wave. The comparator gives out a pulse when sine voltage is greater than the triangular voltage and this pulse is used to trigger the respective inverter switches [4-5]. The ratio between the triangular wave and sine wave must be an integer N, the number of voltage pulses per half-cycle, such that, 2N= fc/fs. The SPWM generation technique is shown in Figure 6.

978-1-4799-0400-6/13/$31.00 ©2013 IEEE

Figure 1. Conventional SPWM generation technique [6].

Amplitude Modulation, and,

Frequency Modulation, Percentage of individual harmonics is calculated by the eqn.

% 100 4√2 1 1

Where, n= nth harmonics. Percentage of total RMS of the output, when is even,

%Vn 100 2α α 2

When is odd,

%Vn 100 2α α 2 α 3

Total harmonics distortion (THD) is given by,

Where, ∑∞ , ,.. or,

And, V1 = Fundamental component.

III. COMPONENTS OF SPWM GENERATING ANALOG CONTROL CIRCUIT

In this segment of the paper different components of the analog switching control circuit have been shown.

Figure 2. Block diagram of SPWM generating control circuit.

To generate the sinusoidal reference signal Wien Bridge Oscillator is used [7]. The output frequency of the oscillator is 50Hz.

Figure 3. Wien Bridge sine wave Oscillator.

Figure 4. Output sine wave (50 Hz) of the Wien Bridge Oscillator.

A single phase shifter is used at the output of Wien Bridge Oscillator to create -1200 phase difference and two phase shifters to create -2400 phase difference [8].

Figure 5. Phase shifter circuit (1200).

Figure 6. Output of -1200 phase shift of Ei.

Output voltage of the phase shifter, θ And the phase angle, θ 2arctan2πf

tan θ2πf 4 When, θ 120 Then, 1μF And, 5.51 KΩ

The frequency of the triangular waveform is generated by the triangular wave generator [8] is 2KHz. The amplitude of carrier triangular wave is controlled by the amplitude of Vsat.

Figure 7. Triangular carrier signal generator.

Figure 8. Triangular carrier signal (2KHz).

The upper limit and lower limit magnitude of the triangular wave respectively are,

5 6

Where, and the frequency of the triangular wave is .

Three individual comparator circuits [8] are used to compare the reference sine waves with the triangular wave.

Figure 9. Op-Amp Comparator circuit.

Figure 12. Comparator output when inputs are sine and triangular wave.

Three inverting amplifier is used [8] at the output of comparator circuit to invert the switching signals.

Figure 10. An inverting amplifier.

Figure 11. Output of Inverting circuit when the input is from comparator

The output voltage of the inverting amplifier is,

7

Whereas, the magnitude of inverting signal must be equal to the output switching signals of comparators,

So, 1 So, .

IV. GENERATION OF SPWM SWITCHING SIGNAL USING ANALOG CONTROL CIRCUIT

Initially three sinusoidal wave reference signals are generated using Wien Bridge Sinusoidal Oscillator circuit. In the next stage, phase difference between the sinusoidal waves and high frequency triangular carrier signal are generated using respectively phase shifter circuit and triangular wave generator. Then using three individual comparator circuits SPWM switching signals g1, g3 and g5 and using three inverting circuits g2, g4, g6 are generated. These SPWM switching signals are applied to the gate of MOSFET of three phase inverter through opt-couplers.

Figure 12. Reference sinusoidal signal and carrier triangular signal.

Figure 13. Individual switching signals (g1,g2,g3,g4,g5,g6).

V. SIMULATION OF INVERTER FOR STANDALONE LOAD

Figure 14. Three phase PWM inverter.

Figure 15. Circuit diagram of analog circuit controlled SPWM three phase

VSI without transformer for Standalone load.

TABLE I. SWITCHING PATTERNS AND LINE TO NEUTRAL VOLTAGES AND LINE TO LINE VOLTAGES AS CO-EFFICIENT OF DC BUS VOLTAGE VS.

For 450V input DC voltage the simulation results such

as, output line to neutral voltages, line to line voltages & current of the inverter have been given below,

Figure 16. Three phase line to line voltage of the inverter (450V).

Switching pattern

Line to neutral voltage

Line to line voltage

g1 g2 g3 Van Vbn Vcn Vab Vbc Vca

0 0 0 0 0 0 0 0 0 1 0 0 2/3 -1/3 -1/3 1 0 -1 1 1 0 1/3 1/3 1/3 0 1 -1 0 1 0 -1/3 2/3 2/3 -1 1 0 0 1 1 -2/3 1/3 1/3 -1 0 1 0 0 1 -1/3 -1/3 -1/3 0 -1 1 1 0 1 1/3 -2/3 -2/3 1 -1 0 1 1 1 0 0 0 0 0 0

Figure 17. Three phase line to neutral voltage (300V).

Figure 18. Three phase current of inverter for resistive load.

Figure 19. Three phase output current for RL load.

VI. SIMULATION OF INVERTER WITH TRANSFORMER The small autonomous regions of power systems, called

micro grids, can offer increased reliability and efficiency and can help to integrate the renewable energy and other forms of distributed generations (DG) [9]. Many forms of DG such as fuel-cells, PV and micro-turbines are interfaced to the network through power electronic converters [10]. Usually, in order to inject energy to the grid, current source inverter (CSI) is used, while in island or autonomous operation voltage source inverter (VSI) is used [11]. To achieve flexible micro grids, which are able to operate in both grid-connected and island mode, VSIs are required [12]. The outputs of an inverter contain large amount of harmonics content. This harmonic attenuation can be achieved by several methods such as by resonating the load, by an LC filter, pulse width modulation, sine wave synthesis, selected harmonic reduction and by polyphase inverters [13]. Moreover in PWM technique, if the carrier frequency is increased, the harmonics components are reduced. A well designed filter can attenuate switching frequency components but impacts on control bandwidth and the impedance presented to grid distortion [14]. RC & LC filters are the most used passive filters. They are divided into 1st order, 2nd Order & 3rd order filters according to the combination of the passive components. LC is a 2nd order filter and LCL is the 3rd order filter.

Figure 20. 3rd order LCL filter for 3 phase system.

In this system Lt is the inductance of the transformer through which the inverter is connected to the grid. After LC filter a transformer is used and the LCL filter is formed. The cut-off frequency of the low pass filter is selected such that, total THD is less than 5%. The calculation is done by the following equation,

12 8

The simulation results of the transformer inputs after filtering and transformer outputs have been given below,

Figure 21. Circuit diagram of 3 phase inverter with transformer.

Figure 22. Three phase line to line voltage after filtering.

Figure 23. Three phase line to neutral voltage after filtering.

Figure 24. Three phase output line to line voltage (11KV) of transformer.

VII. DISCUSSION The DC input voltage of the inverter is 450V. The

MOSFET switches assumed as ideal device. According to the simulation output wave shapes, all the output voltages match with the table.1. The line to neutral peak voltage is 300V AC and line to line peak voltage is 450V AC before filtering. The THD of the output voltage is 91.279672 %. And after filtering the output line to neutral voltage is almost 270V AC and line to line voltage is almost 405V AC, which are less due to some voltage drop to the inductor of the LC filter. The THD is 1.49434693 %.

The fundamental frequency is 50Hz. So the output is pure sinusoidal. The output voltage and frequency can be varied/adjusted by varying the modulation index and

reference sine wave frequency. Moreover, the output line to line voltage of the transformer is 11KV AC, 50 Hz. The transformer is three phase D-Y tap changing transformer.

VIII. CONCLUSION From all the simulation results it is seen that the

designed Op-Amp circuit controlled PWM inverter works accurately. The THD is less than 5% after filtering. The inverter output can be varied by varying the resistance of potentiometer. The inverter responses better for standalone inductive loads like induction motor. If the power is not enough to supply to the grid then it will supply the power to the local standalone loads. If the carrier frequency is increased much enough then the filtering system will be much better and the loss will be less. But better response can be got by using the feedback system, means the closed loop control system. The future work can be done on the feedback loop system.

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